A small single use gas turbine engine with a twin spool rotor shaft and a bypass fan, the rotor shafts being supported for rotation by bearings in the front and rear compartments of the engine. A portion of the bypass fan air is diverted to flow through the bearings in order to provide for cooling of the high speed bearings. Because a large amount of cooling air is required to cool the bearings, an air in tube is positioned in each of the guide vanes in the turbine section to provide for a cooling air passage leading into the rear bearings. In the front bearings, cooling air from the bypass fan is bled off from a location just upstream from the entrance to the centrifugal compressor. A fuel mist tube supplies fuel mist to the cooling air before passing through the bearings to provide extra cooling for the bearings and to provide lubrication to improve the service life of the engine. Because the cooling air is supplied by the bypass fan, the pressure is high enough and the volume is large enough to provide adequate cooling for the high rotational speed bearings used in such a small and high rotating gas turbine engine.